1. Field of the Invention
The present invention generally relates to a method for determining an optical constant of a material suitable for an antireflective layer which is used in the optical lithography process in the fabrication of a semiconductor, and a method for forming a resist pattern.
2. Description of the Prior Art
In accordance with the scale down of design rules for semiconductor devices, it is required to shorten the wavelength of a light source of an exposure system. In the 70 nm design rule, an F2 laser having a wavelength of 157 nm has been considered as the light source, and exposure systems and resists suitable for this light have been developed.
In the optical lithography process, if then resist thickness varies by the coating method (usually, the spin coating) and topography of the underlying substrate, the dimension of a resist pattern or nominal dose varies by the thin film interference. In addition, if the resist is coated on the transparent or substantially transparent and if the thickness of the transparent layer varies by the topography of the layer just below the transparent layer, or if the kind of the under layer is different from place to place, the dimension and nominal dose vary by the thin film interference effect. There is naturally a limit to the improvement of the flatness of the underlying substrate due to the coating uniformity of a resist film, CMP and so forth. In order to cause a semiconductor device to show an expected performance, it is required to confine the above described variation in dimension within a predetermined range. This inversely defines an allowable variation range of the resist thickness, or an allowable variation range of nominal dose which is calculated from it by a lithography process margin.
If the contrast of optical image decreases by the scale down of the pattern, the allowable value of variation in nominal dose also decreases. For that reason, the required levels of the above described coating uniformity and the flatness of the underlying substrate are increased.
According to studies separately carried out by the inventors, even if an exposure system having a numerical aperture NA=0.8 and an illumination coherency σ=about 0.85, and a half-tone mask are used in order to form a pattern in the 70 nm rule by means of a 157 nm light source, the lithography process margin may be only about 8% exposure latitude with 0.2 μm DOF (depth of focus). On these optical conditions, it is predicted that the variation in nominal dose due to the variation in thickness of the resist must be 1% at the maximum, probably 0.5% or less.
Since such materials as aromatic rings, carbon-carbon bonds, carbonyl groups, which constitute a resist, have a strong absorptivity with respect to light having a wavelength of 157 nm, it is actually impossible to use these materials as the materials of the resist for conventional light sources, such as I-line (365 nm light), a KrF laser (248 nm light) and an ArF later (193 nm light).
The relationship between an absorption coefficient α′, an extinction coefficient κ and a transmittance T is herein shown. Assuming that the intensity of transmitted light is I when light entering a material having an optical constant n-iκ at intensity I0 passes through the material by a distance x, the transmittance T is T=I/I0=10−α′x, and an absorption coefficient α′ is expressed by the following expression.                               α          ′                =                              4            ⁢                                                   ⁢            π            ⁢                                                   ⁢            κ            ⁢                                                   ⁢                                          log                10                            ⁡                              (                exp                )                                              λ                                    (        1        )            That is, the transmittance is lower as the transmission distance x is longer, as the extinction coefficient κ (or absorption coefficient α′) is larger, and the wavelength λ is shorter.
In the 157 nm light source, the absorption of 366 nm light and 248 nm light by resist films used for conventional light sources is very high. For example, a typical resist which is used for 248 nm light and which contains a poly-hydroxystyrene derivative as a base resin has an extinction coefficient κ′248nm≈0.01 μm−1 and an absorbance α′248nm<0.22 μm−1, so that absorption is very small. However, with respect to 157 nm light, the resist has very strong absorptivity so as to have κ′157nm≈0.2 μm−1 and an absorbance α′157nm<6.95 μm31 1.
A typical resist which is used for KrF light sources and which contains a hydroxystyrene derivative as a base resin has an absorption coefficient α′=0.22 μm−1 at 248 nm, and has a high transparency so as to have a transmittance of 73.8% even in the case of a resist thickness of 600 nm. On the other hand, with respect to 157 nm light, α′=7-8 μm−1, and the transmittance is only 20% even if the thickness of the resist film is not more than 100 nm. For that reason, the thickness is greatly reduced after development. The transmittance exceeds 70% when the thickness of the resist film is 20 nm or less. on the other hand, the resist pattern also serves as an etching mask for the underlying substrate. Since the thickness of the layer to be processed (the underlying substrate) hardly varies or increases by the scale down of the pattern, the thickness of the resist pattern is preferably as thicker as possible although the lowering of the lithography process margin is limited to an allowable range. In the case of a resist film having a thickness of about 20 nm, it is very difficult to process an underlying substrate even if a hard mask process is used.
Mainly for the above described reasons, a resist material using a fluororesin or a fluorine containing siloxane, which has a high transparency with respect to 157 nm light, as a base resin has been developed. According to reports in documents and societies, a resist film showing relatively high resolution for 157 nm light has an extinction coefficient κ′157 nm=0.04-0.1 and an absorbance α′157=1.04-3.48 μm−1. In order to improve the sensitivity of exposure so as to meet the requirements of a high resolution due to the improvement of dissolution contrast, the light irradiation resistance of the optical system of the exposure tools and a low laser intensity, it is required to increase the amounts of dissolution inhibiting group units and PAG (photo acid generator). As a result of the increase of the amounts of such structure or materials, a resist having an absorption coefficient α′<1 μm−1 (κ≈0.029) is reported to exist. However, since the dissolution inhibiting group units and the PAG have high absorption, even if the resist has a high resolution and a high sensitivity, the absorption coefficient thereof is about α′=1.5-2 μm−1 (κ=0.043-0.058), so that the transparency thereof is far lower than that used for conventional wavelengths. Although resist materials have been subsequently developed, it is difficult to consider that it is possible to obtain high resolution resist materials having a high absorptivity with the same absorption coefficient α′ as conventional wavelengths.
In the optical lithography process, bottom antireflective layers have been generally used. The object of the use of the bottom antireflective layer is as follows. The thickness of the resist on the underlying substrate has the variation in thickness due to the inplane uniformity in the resist coating method and the topography of the underlying substrate produced by processing. And if the transparent layer between substrate and resist (which will be hereinafter referred to as a “transparent substrate”) exist, the thickness or/and the kind of the substrate materials just below transparent substrate has variation in each place. The object of the use of the bottom antireflective layer is to prevent the variation in a desired resist pattern dimension or nominal dose (which will be hereinafter simply referred to as an “nominal dose”) and the irregularities of the side walls of the resist pattern derived from standing waves due to the variation in thickness of the resist film and/or transparent substrate and the like by the thin film interference effect. If it is difficult to suppress the nominal dose only by an interference type bottom antireflective layer, since the variation in thickness of the transparent substrate is large and/or the substrate materials just below transparent substrate are different every place, it is effective to provide a shading film between the underlying transparent substrate and the interference type bottom antireflective layer as disclosed in Japanese Patent Laid-Open No. 8-78322 and so forth.
In an ideal reference reducing coating in the optical lithography process, the side wall of the resist pattern does not have irregularities due to the standing waves, and the nominal dose does not vary due to the variation in thickness of the resist and transparent substrate. The flatness of the side wall of the pattern can be achieved if the reflectance of the interface between the resist film and the bottom antireflective layer is 0 when it is considered to include reflected light from the interface in a lower layer.
However, it is impossible to cause the variation of the nominal dose to be completely 0 since the resist film itself has absorptivity and the inplane variation in thickness of the resist can't be 0. In fact, the allowable value of the variation in nominal dose caused by the variation in thickness of the resist and transparent substrate is determined by a simulative or experimental lithography process margin of desired pattern. Since the optical image deteriorates to lower the lithography process margin with the scale down of the pattern, the range of allowable values of the variation in nominal dose is narrowed, so that it is required to use a bottom antireflective layer having an appropriate optical constant and thickness.
If the resist film has a high transparency, i.e., a very low absorbance α′, the nominal dose of a desired resist pattern fluctuates due to the variation in thickness of the resist film, but the variation of the center line or envelope is very small. FIG. 22 shows the results of calculation of the variation in nominal dose due to the thickness of a resist film AR3produced by Siplay Company and formed on a polysilicon so as to have a thickness of 60 nm, and a resist film when the reflection on the interface between the resist film and the underlying substrate is 0 (i.e. optical constant of resist and underlayer just below to resist is equal, and the thickness of the under layer is thick enough), with respect to 248 nm light. When the transparency of the resist film is high, if the reflectance on the interface between the resist film and the bottom antireflective layer is decreased and if the nominal dose curve approaches a curve on which the reflectance is 0, the variation range of nominal dose due to the variation in thickness of the resist film can be very small. In fact, as described above, since it is impossible to cause the reflection on the interface to be completely 0, it is desired to use a thickness in a region in which the rate of change is small on the nominal dose curve, i.e., in the vicinity of the extreme value, after decreasing the reflectance as lower as possible. For example, when AR3 produced by Siplay Company is formed on a polysilicon so as to have a thickness of 60 nm, if it is assumed that the variation of nominal dose ΔEop=1.5%, the variation of resist thickness ΔTr=15.8 nm is allowable. In addition, if ΔEop=1.0%, ΔTr=12.8 nm is allowable.
FIG. 23 shows an example of the variation of nominal dose due to the variation of resist thickness in the case of 157 nm light. In this figure, “Resist” denotes a resist film, and “BARC” denotes a bottom antireflective layer. This point is the same as that in each of figures which will be described later.
As shown in FIG. 23, in the case of 157 nm light, the increase of the nominal dose due to the increase of the resist thickness is remarkably larger than that in the example of 248 nm light shown in FIG. 22. For that reason, it is impossible to inhibit the variation of nominal dose with respect to the variation of resist thickness by half period or more of vibration components. In the case of 157 nm light, the period of vibration components is shorter than that of 248 nm light in accordance with the period of the standing waves in the film, so that the variation in nominal dose is easy to be great even if the amplitude of the vibration components is the same.
Examples of calculating methods for optical constants and thickness suitable for bottom antireflective layers are disclosed in Japanese Patent Nos. 2897691, 2897692, 2953348 and 2953349.
In the above described prior arts, optical constants of appropriate bottom antireflective layers are calculated with respect to the same thickness of a plurality of resist films with optical constants in the above described range of calculation. Furthermore, the quantity of absorbed light in the prior inventions is associated with the nominal dose in the specification.
However, in these four prior arts, only the materials of the bottom antireflective layers are different, and a method for determining an optical constant and thickness suitable for the bottom antireflective layer is the same. Therefore, although the above described prior arts are effective when the transparency of the resist film is high like the conventional wavelength, there is a problem in that it is not possible to obtain an optical constant suitable for an bottom antireflective layer or it is difficult to automate calculation when the transparency is low like the above described resist film using 157 nm light.
That is, the thickness of the resist film inhibiting the variation in nominal dose varies in accordance with the optical constant of the bottom antireflective layer. In the above described four prior arts, it is considered that it is determined that optical constant of the antireflective layer is suitable only when the range of the thickness of the resist film changed by calculation is sufficiently narrow. In order to obtain an optical constant suitable for a bottom antireflective layer even if the transparency is low, it is required to divide the optical constant of the bottom antireflective layer into a large number of regions to change the thickness of the resist film utilized for calculation for every divided region. However, the above described prior arts fail to disclose such descriptions.
Thus, in a resist film having insufficient transparency, it is required to provide idea different from conventional ides, with respect to the determination of an optical constant of the optimum bottom antireflective layer.